in simple terms a dipole is a two pole antenna which often ( most generally accepted interpretation ) consists of two quarterwave long sections fed at the centre via a coax feed cable the length of the elements being determined by the frequency that you are trying to receive so for example a dipole for Civil airband ( 125Mhz)would have elements 600mm long and one for 300Mhz 250mm long . a simple formula for calculating wavelength in metres is wavelength = 300 divided by frequency in Mhz so for 300Mhz the wavelength is 1metre and so a quarter wavelength is therefore 250mm

The elements can be made from tube (copper brass or aluminium are all suitable for loft mounted versions )or wire . if the antenna is for mounting outside aluminium is the preferred material as it is less effected by the weather and is light in weight . external antennas will need to have waterproofing applied to the feedpoint to ensure no water enters the cable . This can be in the form of a waterproof enclosure for either the whole antenna or just the feedpoint . White PVC conduit fittings available at most diy stores is suitable (grey or black pvc contains a filler which may attenuate the signal so is not recommended ) here is one I made earlier

The coax feed is fed through the conduit and soldered to the elements inside the centre T section the horizontal section between the antenna and the short support mast needs to be greater than 1/2 wavelength so that the feeder does not detune the antenna

you will need a male BNC plug on the end of the cable to connect to the female socket on the UBC125xlt antenna connector

A UHF TV antenna will work on a scanner but will not be very effective on frequencies it was not designed to receive and they are generally very directional . It may however, due to the additional height be better than a rubber duck fitted on the RX on some frequencies try it and see it wont cost you anything apart from a short patch lead with suitable adaptors from the TV aerial feed point to your RX . My earliest antenna experiments consisted of using my steel bed frame as an aerial for radio Luxembourg ( 208m MW ) in the late 50s (which when coupled to a valve radio with 200vdc HT on the aerial socket could have been lethal but I survived )

Use a frequency at the middle of the desired band. But don't expect it to be as good as you move away from that centre frequency. So Airband being a big band is not as good for a single dipole as say Marine band.

To optimize the antenna for a frequency RANGE, do the calculations twice, once for the low end of the range and once for the high end; then average the two .

Edited to add..

A halfwave dipole is slightly less than half a wavelength, due to the physics that I will not confuse you with.

Having tried many homebrew antennas for Civil Airband reception I was surprised to find that a simple vertical halfwave dipole with each half having a length of 600mm was in practical terms as good as was required for my purposes and allows me to monitor virtually the whole band . The dipole picking up the same transmissions as a D777 which according to many is the best available commercial wideband antenna for Airband(s) monitoring . I have recently built a Slim jim antenna designed for 128Mhz which due in part to its low angle of radiation is better at receiving some parts of the civil airband even though it has in theory a narrower band width than the dipole (in theory the slimjim has a few Dbs gain over a dipole at its design frequency ) .

I have not had much success with Multiple dipoles such as that described by Alan for VHF and UHF ( see his link ) as I think due to their proximity to each other a certain amount of detuning occurs (when compared to the HF versions which can be effective )

The military airband being much wider ie approx 220-390 Mhz is a different kettle of fish which is why the discone is commonly used by the professional users of the band and can be seen atop many military base control towers in the UK . Increasing the diameter of the tube used to construct a dipole for the centre of the band ie 300Mhz to 40mm may increase the bandwidth slightly, however the most popular HOMEBREW antenna amongst military airband listeners for their base station antenna is the bowtie which consists of two 80cm lengths of stiff wire each bent into a V shape with the open end of the V having a gap of 34 cm and the pointed end of the V crimped and inserted into a piece of choc block to which the coax is connected (see below) . the elements are mounted vertically and according to several theorists if the angle between each of the two Vs is 130 degrees the antenna is resonant on a very wide portion of the VHF and UHF spectrum and some say is as good as a discone which is resonant across a very wide bandwidth eg 100 -900 Mhz NB the discone has no gain over a dipole but they do have a much wider bandwidth

The bowtie is a 2D version of the Bicone which can be found described as a double discone in some circles

my bicone for anyone interested along with a couple of logperiodics in the background